Cumulative distribution function: Difference between revisions

→‎Definition: clarify phrasing
(→‎Definition: clarify phrasing)
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In the definition above, the "less than or equal to" sign, "≤", is a convention, not a universally used one (e.g. Hungarian literature uses "<"), but the distinction is important for discrete distributions. The proper use of tables of the [[Binomial distribution|binomial]] and [[Poisson distribution]]s depends upon this convention. Moreover, important formulas like [[Paul Lévy (mathematician)|Paul Lévy]]'s inversion formula for the [[Characteristic function (probability theory)#Inversion formulae|characteristic function]] also rely on the "less than or equal" formulation.
If treating several random variables <math>X,Y,\ldots</math> etc. the corresponding letters are used as subscripts while, if treating only one, the subscript is usually omitted. It is conventional to use a capital <math>F</math> for a cumulative distribution function, in contrast to the lower-case <math>f</math> used for [[probability density function]]s and [[probability mass function]]s. This applies when discussing general distributions: some specific distributions have their own conventional notation, for example the [[normal distribution]].